Mathematics · Year 3

Active learning ideas

Growing Patterns

Active learning with manipulatives and movement builds concrete understanding of growing patterns. Students see the steady increase in quantities rather than just symbols on a page. This tactile experience supports all learners, especially those who need visual or kinesthetic reinforcement.

• ACARA Content Descriptions
• AC9M3A01

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 30 min · Small Groups

Manipulative Build: Linking Cube Patterns

Provide unifix cubes or linking blocks. Students start with a given first term and rule, such as 3 then add 2, to build the first four terms. They predict and add the next three terms, then explain the rule to their group. Groups share one pattern with the class for predictions.

Explain the rule that governs a given growing pattern.

Facilitation Tip

During Manipulative Build, circulate to ask students to explain their rule aloud before they write it down.

What to look for

Present students with a pattern like 5, 10, 15, 20. Ask: 'What is the rule for this pattern?' and 'What are the next two numbers in the pattern?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 25 min · Whole Class

Human Number Line: Growing Steps

Mark a floor number line. Select students to stand at positions representing pattern terms, like 5, 8, 11. The class calls out the rule and directs the next three positions. Switch roles so all students participate in moving and predicting.

Design a growing pattern that increases by a constant amount each step.

Facilitation Tip

For the Human Number Line, step out the pattern physically so students feel the steady increase in their bodies.

What to look for

Give each student a card with a different growing pattern (e.g., add 4, add 1). Ask them to write down the rule and the next three terms for their specific pattern.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Prediction Cards: Pattern Challenges

Prepare cards showing partial patterns, such as 1, 4, __, __. In pairs, students write the rule, fill gaps, and predict three more terms. Pairs swap cards to check predictions and discuss rule differences.

Predict the next three terms in a growing pattern based on its rule.

Facilitation Tip

In Prediction Cards, have students swap cards with a partner and explain their rule before revealing the next term.

What to look for

Show a visual pattern of dots increasing by 3 each time. Ask: 'How can you describe the rule in words?' and 'If this pattern continued for 5 more steps, how many dots would there be in total?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 35 min · Individual

Design Station: Custom Pattern Art

At stations with beads, paper, or tiles, students design a growing pattern artwork that increases by a constant, like adding one shape per step. Label the rule and next terms. Rotate to extend a peer's pattern.

Explain the rule that governs a given growing pattern.

Facilitation Tip

At the Design Station, prompt students to label their art with both a word rule and a symbol rule.

What to look for

Present students with a pattern like 5, 10, 15, 20. Ask: 'What is the rule for this pattern?' and 'What are the next two numbers in the pattern?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach growing patterns by starting concrete, moving to representational, then abstract. Avoid rushing to symbols before students can explain growth in words or show it with objects. Research shows that students who work with physical models before symbols develop stronger reasoning skills. Use consistent vocabulary like 'each step grows by' to reinforce the constant change.

Students will confidently identify addition rules for growing patterns, predict multiple terms, and create their own original sequences. They will articulate rules in words or symbols and justify their reasoning to peers. Lessons are successful when the class moves from guessing to evidence-based predictions.

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Watch Out for These Misconceptions

• During Manipulative Build, watch for students who assume patterns always multiply by building stacks that double in height each time.

  Ask these students to count the cubes in each tower aloud and compare differences. Have them record the total cubes at each step to see the +3 increase, then rebuild with that rule.

• During Human Number Line, watch for students who think the rule changes if the steps feel different.

  Have the class repeat the same pattern three times in a row while naming each step aloud. Compare the final positions to show the rule stayed constant.

• During Design Station, watch for students who create repeating shapes instead of growing sequences.

  Prompt them to add one more element to each shape and count the new total. Ask, 'How many more dots are here than in the last picture?' to refocus on numerical growth.

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Methods used in this brief

• Think-Pair-Share